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EAMCET Engineering 2002 Solved Paper

Section: Mathematics

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Question : 123 of 200

Marks: +1, -0

If

P=(0,1,0), Q=(0,0,1)

, then the projection of

P Q

x+y+z=3

2
$\sqrt{2}$
3
$\sqrt{3}$

Solution:

Direction ratios of

P Q

\;=(0-0,0-1,1-0)=(0,-1,1)

\;\text{ Direction cosine }\;= \left(|0|,\left| -\frac{1}{\sqrt{2}} \right|,\left| \frac{1}{\sqrt{2}} \right|\right)

The given plane is

x+y+z=3

Direction ratios of the plane are

(1,1,1)

Length of the projection

\;=0 \cdot 1+1 \cdot \frac{1}{\sqrt{2}}+1 \cdot \frac{1}{\sqrt{2}}

\;=\frac{2}{\sqrt{2}}=\sqrt{2}

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